Searching for just a few words should be enough to get started. If you need to make more complex queries, use the tips below to guide you.
Article type: Research Article
Authors: Briet, Philippe | Raikov, Georgi | Soccorsi, Eric
Affiliations: Centre de Physique Théorique, CNRS-Luminy, Case 907, 13288 Marseille, France. E-mails: {briet, soccorsi}@cpt.univ-mrs.fr | Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago de Chile, Chile. E-mail: graikov@mat.puc.cl
Abstract: We consider a 2D Schrödinger operator H0 with constant magnetic field, on a strip of finite width. The spectrum of H0 is absolutely continuous, and contains a discrete set of thresholds. We perturb H0 by an electric potential V which decays in a suitable sense at infinity, and study the spectral properties of the perturbed operator H=H0+V. First, we establish a Mourre estimate, and as a corollary prove that the singular continuous spectrum of H is empty, and any compact subset of the complement of the threshold set may contain at most a finite set of eigenvalues of H, each of them having a finite multiplicity. Next, we introduce the Krein spectral shift function (SSF) for the operator pair (H, H0). We show that this SSF is bounded on any compact subset of the complement of the threshold set, and is continuous away from the threshold set and the eigenvalues of H. The main results of the article concern the asymptotic behaviour of the SSF at the thresholds, which is described in terms of the SSF for a pair of effective Hamiltonians.
Keywords: Schrödinger operators, magnetic field, Mourre estimates, spectral shift function, effective Hamiltonians
Journal: Asymptotic Analysis, vol. 58, no. 3, pp. 127-155, 2008
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
USA
Tel: +1 703 830 6300
Fax: +1 703 830 2300
sales@iospress.com
For editorial issues, like the status of your submitted paper or proposals, write to editorial@iospress.nl
IOS Press
Nieuwe Hemweg 6B
1013 BG Amsterdam
The Netherlands
Tel: +31 20 688 3355
Fax: +31 20 687 0091
info@iospress.nl
For editorial issues, permissions, book requests, submissions and proceedings, contact the Amsterdam office info@iospress.nl
Inspirees International (China Office)
Ciyunsi Beili 207(CapitaLand), Bld 1, 7-901
100025, Beijing
China
Free service line: 400 661 8717
Fax: +86 10 8446 7947
china@iospress.cn
For editorial issues, like the status of your submitted paper or proposals, write to editorial@iospress.nl
如果您在出版方面需要帮助或有任何建, 件至: editorial@iospress.nl